week1-2

# week1-2 - Normal NormalStress avg F = A shorten...

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ormal Stress Normal Stress F A avg σ Force serves to lengthen or shorten Stress acts on a surface perpendicular to the direction of e internal force the internal force

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xial Strain Axial Strain length change in L e Δ ength original l L L = = = ε
xial ress and Strain Axial Stress and Strain Sign convention ε and σ are positive in tension nd e egative ε and σ are negative in compression Mechanics of Materials Beer, Johnston DeWolf (2006)

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ear Stress Shear Stress ress acts on a surface arallel the Stress acts on a surface parallel to the direction of the internal force rce serves to “cut” Force serves to cut A V = avg τ V
uality of Shear Stresses (1) Equality of Shear Stresses (1) From Statics Sum of the forces in the x direction is zero From Solid Mech Force = Stress×Area yx yx x z x z x F τ = Δ Δ Δ Δ = 0 yx yx =

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uality of Shear Stresses (2) Equality of Shear Stresses (2) From Statics Sum of the forces in the y direction is zero From Solid Mech Force = Stress×Area xy xy y z y z y F τ = Δ Δ Δ Δ = 0 xy xy =
uality of Shear Stresses (3) Equality of Shear Stresses (3) ( ) ( ) y z x x z y M xy xy z Δ Δ Δ Δ Δ Δ = τ yx xy z M = = 0 Overall = = = = yx xy yx xy

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ear rain Shear Strain θ π γ = x δ 2 L = units of γ = radians
ear ress and Strain Shear Stress and Strain +ve -ve Sign convention 0 ( 0) if i ll th ii l γ >0, ( τ >0), if θ ’ is smaller than original θ γ <0, ( τ <0), if θ ’ is larger than original θ

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xial Load, Shear Stress Axial Load, Shear Stress One set of internal axes shows axial deflection in response an axial deflection in response to the load Another set of internal axes shows a shear deflection in response to the load Mechanics of Materials Beer, Johnston DeWolf (2006)
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week1-2 - Normal NormalStress avg F = A shorten...

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